A330711 - OEIS

%I #12 Dec 28 2019 14:18:30

%S 1,2,4,6,12,16,30,36,48,55,60,72,78,84,90,102,105,126,144,156,168,180,

%T 184,192,208,238,240,252,264,304,315,320,322,344,360,370,378,396,430,

%U 432,488,528,536,540,576,590,605,609,621,639,648,657,660,672,680,702

%N Numbers that are both Zeckendorf-Niven numbers (A328208) and lazy-Fibonacci-Niven numbers (A328212).

%H Amiram Eldar, <a href="/A330711/b330711.txt">Table of n, a(n) for n = 1..10000</a>

%e 6 is in the sequence since A007895(6) = 2 and A112310(6) = 3, and both 2 and 3 are divisors of 6.

%t zeckSum[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]];

%t fibTerms[n_] := Module[{k = Ceiling[Log[GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k--]; fr];

%t dualZeckSum[n_] := Module[{v = fibTerms[n]}, nv = Length[v]; i = 1; While[i <= nv - 2, If[v[[i]] == 1 && v[[i + 1]] == 0 && v[[i + 2]] == 0, v[[i]] = 0; v[[i + 1]] = 1; v[[i + 2]] = 1; If[i > 2, i -= 3]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, 0, Total[v[[i[[1, 1]] ;; -1]]]]];

%t Select[Range[1000], Divisible[#, zeckSum[#]] && Divisible[#, dualZeckSum[#]] &]

%Y Intersection of A328208 and A328212.

%Y Cf. A007895, A014417, A104326, A112310.

%K nonn

%O 1,2

%A _Amiram Eldar_, Dec 27 2019